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Theorem dfss5 3461
 Description: Another definition of subclasshood. Similar to df-ss 3259, dfss 3260, and dfss1 3460. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
dfss5 (A BA = (BA))

Proof of Theorem dfss5
StepHypRef Expression
1 dfss1 3460 . 2 (A B ↔ (BA) = A)
2 eqcom 2355 . 2 ((BA) = AA = (BA))
31, 2bitri 240 1 (A BA = (BA))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642   ∩ cin 3208   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by: (None)
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